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<H3>improper_style cossq command 
</H3>
<H3>improper_style cossq/omp command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>improper_style cossq 
</PRE>
<P><B>Examples:</B>
</P>
<PRE>improper_style cossq
improper_coeff 1 4.0 0.0 
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>cossq</I> improper style uses the potential
</P>
<CENTER><IMG SRC = "Eqs/improper_cossq.jpg">
</CENTER>
<P>where x is the improper angle, x0 is its equilibrium value, and K is a
prefactor.  
</P>
<P>If the 4 atoms in an improper quadruplet (listed in the data file read
by the <A HREF = "read_data.html">read_data</A> command) are ordered I,J,K,L then X
is the angle between the plane of I,J,K and the plane of J,K,L.
Alternatively, you can think of atoms J,K,L as being in a plane, and
atom I above the plane, and X as a measure of how far out-of-plane I
is with respect to the other 3 atoms.
</P>
<P>Note that defining 4 atoms to interact in this way, does not mean that
bonds necessarily exist between I-J, J-K, or K-L, as they would in a
linear dihedral.  Normally, the bonds I-J, I-K, I-L would exist for an
improper to be defined between the 4 atoms.
</P>
<P>The following coefficients must be defined for each improper type via
the <A HREF = "improper_coeff.html">improper_coeff</A> command as in the example
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>K (energy/radian^2)
<LI>X0 (degrees) 
</UL>
<P>X0 is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian^2.
</P>
<HR>

<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
the same as the corresponding style without the suffix.  They have
been optimized to run faster, depending on your available hardware, as
discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
manual.  The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.
</P>
<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
packages, respectively.  They are only enabled if LAMMPS was built with
those packages.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info.
</P>
<P>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
switch</A> when you invoke LAMMPS, or you can
use the <A HREF = "suffix.html">suffix</A> command in your input script.
</P>
<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
more instructions on how to use the accelerated styles effectively.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>This improper style can only be used if LAMMPS was built with the
USER-MISC package.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info on packages.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "improper_coeff.html">improper_coeff</A>
</P>
<P><B>Default:</B> none
</P>
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